Causality detection and quantification by ensembles of time delay neural networks for application to nuclear fusion reactors

The understanding and control of complex systems in general, and thermonuclear plasmas in particular, require analysis tools, which can detect not the simple correlations but can also provide information about the actual mutual influence between quantities. Indeed, time series, the typical signals collected in many systems, carry more information than can be extracted with simple correlation analysis. The objective of the present work consists of showing how the technology of Time Delay Neural Networks (TDNNs) can extract robust indications about the actual mutual influence between time indexed signals. A series of numerical tests with synthetic data prove the potential of TDNN ensembles to analyse complex nonlinear interactions, including feedback loops. The developed techniques can not only determine the direction of causality between time series but can also quantify the strength of their mutual influences. An important application to thermonuclear fusion, the determination of the additional heating deposition profile, illustrates the capability of the approach to address also spatially distributed problems.